A common problem in biomedical research is to describe a response (Y) as a function of explanatory variables (X). When observations are independent, generalized linear models (GLM's) including linear, logistic, log-linear and proportional hazards models are well developed for this purpose. When observations are correlated, current techniques are inadequate, particularly for discrete and non-normal outcomes. This study will develop regression methods for correlated data which arise in longitudinal and time series studies. In longitudinal studies, a few observations are made on each of many subjects. Repeated valves for an individual are correlated. In time series studies, inferences about the relationship of Y and X are made from a single longer set of correlated observations. By developing extensions of GLM's, the methods will be useful for a variety of discrete and continuous responses common to biomedical and particularly infectious disease research. For longitudinal studies, I will develop transitional, marginal and random effects (mixed) models. These will be used to analyze longitudinal data from the Multicenter AIDS Cohort Study (MACS), the Haiti HIV Study (HHS) and a study of infectious diseases and Vitamin A deficiency in Indonesian children (ICS). For the time series case, parameter and observation driven models (Cox, 1981) will be studied. These models will be used to estimate trends and make short-term projections of AIDS incidence by risk group and state in the U.S. and of hepatitis incidence by county in the State of Pennsylvania.